Abstracts
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Encoding a qubit in a spin
Presenting Author: Jonathan Gross, Google
I present a new approach for designing quantum error-correcting codes that guarantees a physically natural implementation of Clifford operations. Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in an oscillator, in which Clifford operations may be performed via Gaussian unitaries, this approach yields new schemes for encoding a qubit in a large spin in which single-qubit Clifford operations may be performed via spatial rotations. I construct all possible examples of such codes, provide universal-gate-set implementations using Hamiltonians that are at most quadratic in angular-momentum operators, and derive criteria for when these codes exactly correct physically relevant noise channels to lowest order. This technique yields a minimal eight-dimensional code in spin-7/2 that exactly corrects these errors, analogous to a perfect block code.
Read this article online: https://doi.org/10.1103/PhysRevLett.127.010504
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